Maths · Applications of derivatives: Rate of change of quantities, monotonic-Increasing and decreasing functions, Maxima and minima of functions of one variable
=\tan ^{-1} x-x \) is
\( f(x)=\tan ^{-1} x-x \) is \( _{-1} \) \( \boldsymbol{R} \)
- A. increasing to \( R \)
- B. decreasing to \( R \)
- C. increasing on \( R^{+} \)
- D. increasing on \( (-\infty, 0) \)
Step-by-step solution
Compute f'(x) = 1/(1+x^2) - 1 = -x^2/(1+x^2) ≤ 0 for all real x, with equality only at x=0. Hence f is decreasing on entire R.
Related MCQs
- If the ratio of base radius and height of a cone is 1: 2 and percentage error in radius is then the error in its volume is…
- Function =(\boldsymbol{x}+\mathbf{2}) \boldsymbol{e}^{-\boldsymbol{x}} \) is…
- The two curves and…
- Equation of normal drawn to the graph of the function defined as =\frac{\sin x^{2}}{x} \) and =\mathbf{0} \) at the origin is?…
- If the radius of a sphere is measured as with an error of then, find the approximate error in calculating its volume…